1. Field of the Invention
This invention relates to a method of damping an actuator, provided with a piezoelectric element and a displacement enlargement mechanism, and an actuator having a damping mechanism.
2. Description of the Related Art
A lamination-type piezoelectric element is a driving element that is very effective for high-precision positioning. The lamination-type piezoelectric element includes piezoelectric materials represented by, for example, PZT (PbZrO3—PbTiO3), which has excellent high-speed responsiveness and can generate great force and which are stacked in many layers. However, the amount of displacement of this piezoelectric element for drive is very small or about 1/1,000 of the height of the lamination. If a substantial shear load acts on the piezoelectric element itself, there is a problem that adhesive surfaces of the piezoelectric materials are liable to break. Thus, it is necessary to take account of methods of fixing and supporting the piezoelectric element, connection with parts to be driven, etc. If the simple piezoelectric element is to be used as an actuator, therefore, it is very hard to employ it.
Accordingly, there is proposed an actuator in which a lamination-type piezoelectric element is combined with a displacement enlargement mechanism that geometrically enlarges a small displacement generated by the piezoelectric element and, at the same time, facilitates attachment to fixing portions and parts to be driven. Described in PI-Politic Catalog-2001, issued in July 2000, Germany, pp. 2-16, for example, is a displacement enlargement mechanism that enlarges a displacement of a piezoelectric element by a lever mechanism. Described in the Catalog “CEDRAT TECHNOLOGIES,” September 2002, France, p. 56, is a mechanism that extends the diagonals of a rhombic body formed of four elastic hinges, whereby the enlarging ratio shows the ratio between the two diagonal lengths. Described in PI-Politic Catalog-2001, issued in July 2000, Germany, pp. 2-42, is an applicative mechanism that squeezes in a wedge-shaped end by extending a piezoelectric element, thereby enlarging a displacement. Further, an actuator that uses a link mechanism as a displacement enlargement mechanism is proposed in Jpn. Pat. Appln. KOKAI Publication No. 6-28805. The actuator of this type is widely used in the field of industrial devices that require precise positioning.
The greatest advantage of an actuator that comprises a displacement enlargement mechanism and a piezoelectric element is that a characteristic of the actuator can be expressed by a second order lag element that can be represented by one spring, a damper, and a mass, and that high controllability is ensured by one main resonance in a high frequency bandwidth. If the responsiveness is improved, however, the main resonance peak tends to become higher. If a control system of the actuator is constructed with the resonance peak amplitude at a high value, a servo bandwidth (a gain crossover frequency) indicated by frequency that reaches to the zero-cross point is restricted in an open-loop characteristic and constitutes a factor to degrade the control performance. Generally, therefore, an attempt is made that the resonance frequency is within as high a bandwidth as possible to improve the control system, thereby extending the servo bandwidth.
The resonance frequency of the second order lag element indicates fulfills the following expression:
            ω      ⁢                          ⁢      n        ∝                  k        m              ,where m is the mass of the actuator and k is a spring constant. In this expression, moreover, ωn is a natural angular frequency of the system, and a resonance frequency f is f=ωn/2π.
If the mass of the actuator, that is, the mass of a movable portion, is fixed, the spring stiffness of the displacement enlargement mechanism must be enhanced to increase the resonance frequency of the actuator.
On the other hand, the displacement of the lamination-type piezoelectric element is substantially in inverse proportion to the generated force, so that the extension of the piezoelectric element must be reduced, as the generated force increases. If the spring constant is enhanced to increase the resonance frequency, therefore, a maximum displacement amount of the actuator is lessened inevitably. The relationship between the resonance frequency and the maximum displacement amount of the actuator is trade-off to each other, and it is very difficult for them to be compatible with each other.
The actuator constructed in this manner can be easily handled as a mechanical part. Mechanically, it is configured so that the displacement can be enlarged. Actually, in order to achieve compatibility with a high resonance frequency, however, the actuator can generate only the maximum displacement amount that is substantially equal to a no-load maximum displacement amount of the used simple lamination-type piezoelectric element, in many cases. With the actuator that is formed by combining the displacement enlargement mechanism and the lamination-type piezoelectric element, some design conditions naturally restrain the resonance frequency from being unlimitedly increased without failing to secure a desired maximum displacement amount in order to improve the control performance. This produces a serious problem in constructing a high-speed, high-accuracy control system.
In extending the control bandwidth of the control system by mechanical improvement, in the actuator that comprises the lamination-type piezoelectric element and the displacement enlargement mechanism, the resonance frequency is increased to a higher bandwidth or the damping performance is enhanced to lower the resonance peak amplitude lest the peak amplitude of the resonance frequency exceed a cross line of 0 dB and make the system unstable.
If the improvement is to be made based on the design of the control system, on the other hand, a conventional PID (proportional-integral-derivative) controller generally cancels the resonance peak with antiresonance characteristics given by a narrow-bandwidth notch filter. Since the notch filter causes a phase inversion at the same time, however, the control performance cannot be enhanced fundamentally.
Further, the frequency can be shaped with an H∞ that has a robust control performance, and the resonance peak amplitude can be canceled with the antiresonance characteristics without influencing the phase characteristics. However, the control system becomes a high order and is complicated. Therefore, the cancellation of the resonance peak amplitude cannot be easily realized without using a control system design CAD (MATLAB) or a DPS (digital signal processor) that is expensive although having high-speed calculation capacity. If high-speed performance is required, as is the case with the actuator, moreover, the computation capacity of the existing DSP cannot realize a desired controller, depending on the order number of the control system. Unlike the PID controller, furthermore, robust controllers, such as the H∞ that can be realized by the DSP using the CAD, cannot be easily adjusted based on a personal experience or feeling, so that they are prevented from becoming prevalent.
Thus, improving the damping capacity of the actuator itself to lower its resonance peak is a fundamental improvement necessary for the enhancement of the control bandwidth and is the most effective countermeasure. Conventionally, a damping material, such as rubber or paper, is sandwiched between fixing portions and a support portion of an actuator, and vibrational energy in the actuator is converted into thermal energy by contact friction between parts or fastening screw surfaces, whereby the resonance peak is damped. By lowering the fastening force of the fixing portions of the actuator, moreover, the contact friction at the support portion of the actuator can be increased, and vibrational energy generated by resonance can be converted into thermal energy to be damped so that the resonance peak is lowered. If this is done, on the other hand, the resonance frequency also lowers inevitably, in general. As one of methods that are effective although not essential, there is a technique in which the tightening torque of fixing screws is controlled, so that the resonance peak can be made as low as possible without failing to keeping the resonance frequency high.
However, a damping force that is generated by this technique is not very large but only serves to adjust the resonance peak not to be unduly high. If an elastic or viscoelastic body, such as a damping material, is sandwiched between the fixing portions, the positioning accuracy is adversely affected when the actuator is mounted with the fixing portions used as references. Thus, this technique is not desirable as a fixing method for the actuator in which precision positioning is essential.